Prawf: An Interactive Proof System for Program Extraction

Berger, Ulrich; Petrovska, Olga; Tsuiki, Hideki

doi:10.1007/978-3-030-51466-2_12

Cited by 4 publications

(7 citation statements)

References 4 publications

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“…IFP supports the extraction of lazy functional programs from inductive/coinductive proofs in intuitionistic first order logic. It has an implementation called Prawf [6], and its extracted programs can be directly translated into Haskell for execution [8]. Each formula A of IFP (and of CFP) translates into a predicate R(A) on a Scott domain D defining the set of realizers of A. R(A) can be viewed as a specification of the programs solving the computational problem expressed by A.…”

Section: Introductionmentioning

confidence: 99%

Extracting total Amb programs from proofs

Berger¹,

Tsuiki²

2021

Preprint

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We present a logical system CFP (Concurrent Fixed Point Logic) from whose proofs one can extract nondeterministic and concurrent programs that are provably total and correct with respect to the proven formula. CFP is an intuitionistic first-order logic with inductive and coinductive definitions extended by two propositional operators, A || B (restriction, a strengthening of the implication B → A) and (A) (total concurrency). The target of the extraction is a lambda calculus with constructors and recursion extended by a constructor Amb (for McCarthy's amb) which is interpreted operationally as globally angelic choice. The correctness of extracted programs is proven via an intermediate domain-theoretic denotational semantics. We demonstrate the usefulness of our system by extracting a concurrent program that translates infinite Gray code into the signed digit representation. A noteworthy feature of our system is that the proof rules for restriction and concurrency involve variants of the classical law of excluded middle that would not be interpretable computationally without Amb.

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Section: Introductionmentioning

confidence: 99%

Extracting total Amb programs from proofs

Berger¹,

Tsuiki²

2021

Preprint

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“…PRAWF: An Interactive Proof System for Program Extraction [22] (by U. Berger, O. Petrovska, H. Tsuiki) This paper presents an interactive proof system dedicated to program extraction from proofs. The implementation uses an updated version of IFP presented in [24].…”

Section: Optimized Program Extraction For Induction and Coinductionmentioning

confidence: 99%

“…Although the examples are small, they are appropriately simple to present how programs are extracted at a reasonable level of detail. A more complex case study was done by Tsuiki and it is presented in [22].…”

Section: Structure Of the Thesismentioning

confidence: 99%

“…This chapter gives a walk-through from the stage when a proof is constructed to the stage wh en an extracted program is executed. We present a couple of simple programs in detail and outline a more complex example, a program for exact real numbers representations, which was presented in [22].…”

Section: Case Studiesmentioning

confidence: 99%

“…This proof is included with PRAWF distribution. The most interesting points of the proof are highlighted in [22]. Should the reader be interested, the distribution also contains a few more tactics, which can be used to extract some simpler programs.…”

Section: Summary and More Complex Case Studies Working On These Examples Hasmentioning

confidence: 99%

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Enhanced Realizability Interpretation for Program Extraction

Petrovska¹

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This thesis presents Intuitionistic Fixed Point Logic (IFP), a schema for formal systems aimed to work with program extraction from proofs. IFP in its basic form allows proof construction based on natural deduction inference rules, extended by induction and coinduction. The corresponding system RIFP (IFP with realiz-ers) enables transforming logical proofs into programs utilizing the enhanced re-alizability interpretation. The theoretical research is put into practice in PRAWF1, a Haskell-based proof assistant for program extraction.

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Extracting total Amb programs from proofs

Berger

Tsuiki

2022

Lecture Notes in Computer Science

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We present a logical system CFP (Concurrent Fixed Point Logic) that supports the extraction of nondeterministic and concurrent programs that are provably total and correct. CFP is an intuitionistic first-order logic with inductive and coinductive definitions extended by two propositional operators, $$B|_{A}$$ B | A (restriction, a strengthening of implication) and $${\mathbf {\downdownarrows }}(B)$$ ⇊ ( B ) (total concurrency). The source of the extraction are formal CFP proofs, the target is a lambda calculus with constructors and recursion extended by a constructor Amb (for McCarthy’s amb) which is interpreted operationally as globally angelic choice and is used to implement nondeterminism and concurrency. The correctness of extracted programs is proven via an intermediate domain-theoretic denotational semantics. We demonstrate the usefulness of our system by extracting a nondeterministic program that translates infinite Gray code into the signed digit representation. A noteworthy feature of our system is that the proof rules for restriction and concurrency involve variants of the classical law of excluded middle that would not be interpretable computationally without Amb.

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Prawf: An Interactive Proof System for Program Extraction

Cited by 4 publications

References 4 publications

Extracting total Amb programs from proofs

Extracting total Amb programs from proofs

Enhanced Realizability Interpretation for Program Extraction

Extracting total Amb programs from proofs

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